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Unit Circle Ratios

Unit Circle Ratios
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2015-11-30 17:10
CircleFunctionTrigonometry
This example visually demonstrates the six trigonometric ratios and their associated graphs using the unit circle. It helps to understand concepts like sine, cosine, tangent, cotangent, secant, and cosecant. Commands used include Circle, Segment, Tangent, Angle, and Function. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Point(yAxis) → B
  3. Circle(A, B) → c
  4. Intersect(c, xAxis, 2) → C
  5. Segment(A, C) → d
  6. Point(c) → D
  7. OrthogonalLine(D, d) → f
  8. Tangent(D, c) → e,
  9. Intersect(xAxis, e) → E
  10. Segment(E, A) → m
  11. Angle(C, A, D) → θ
  12. Segment(A, D) → b
  13. Intersect(e, yAxis) → F
  14. Segment(F, D) → cotα
  15. Segment(D, E) → tanα
  16. Segment(A, F) → cscα
  17. Intersect(f, m) → H
  18. Segment(D, H) → sinα
  19. Segment(A, E) → secα
  20. Segment(A, H) → cosα
  21. OrthogonalLine(D, sinα) → i
  22. Function(1 / sin((2 * (x - (2 * 3.14 / 3)))), 2.09, 5.24) → cosecantα
  23. Intersect(cosecantα, h, (2.495559497562619, 1.3880195691190431)) → G
  24. Function(sin((2 * (x - (2 * 3.14 / 3)))), 2.09, 5.24) → sineα
  25. Intersect(sineα, h, (2.495559497562619, 0.7204509376151564)) → I
  26. Function(tan((2 * (x - (2 * 3.14 / 3)))), 2.09, 5.24) → tangentα
  27. Intersect(tangentα, h, (2.495559497562619, 1.0388533504365465)) → J
  28. Function(cos((2 * (x - (2 * 3.14 / 3)))), 2.09, 5.24) → cosineα
  29. Intersect(cosineα, h, (2.495559497562619, 0.6935059094841528)) → K
  30. Function(1 / cos((2 * (x - (2 * 3.14 / 3)))), 2.09, 5.24) → secantα
  31. Intersect(secantα, h, (2.495559497562619, 1.4419487798508095)) → L
  32. Function(1 / tan((2 * (x - (2 * 3.14 / 3)))), 2.09, 5.24) → cotangentα
  33. Intersect(cotangentα, h, (2.495559497562619, 0.9625997736637038)) → M
  34. Function(0, 1.9, 5.5) → g
  35. Segment(A, C) → a
  36. Segment(H, D) → j
  37. Segment(A, F) → k
  38. Segment(F, E) → l
  39. Intersect(j, m) → N
  40. Intersect(m, l) → O
  41. Intersect(k, l) → P
  42. Function(1, 1.9, 5.5) → p
  43. Function(-1, 1.9, 5.5) → q
  44. CircleArc(A, C, D) → f_1
  45. Intersect(sineα, tangentα, (2.0933273569696556, -1.195272735515079E-5)) → Q
  46. Intersect(g, h, 1) → R
  47. Segment(Q, R) → g_1